The transfer of heat in tubular heat exchangers is an operation that has widespread application in all industries, particularly in the process and power industries. As energy and capital costs have increased, the need for improving the efficiency of heat transfer surfaces has taken on greater importance. Because the cost of heat exchangers employing heat transfer tubes depends in substantial part upon the number of tubes used in the heat exchangers, it is highly desirable that the amount of tubing required to provide a given heat transfer be reduced. Furthermore, since the temperature of the tube wall is determined by the surface heat transfer coefficients on the inside and outside surfaces of the tube wall for given stream conditions, preferential control over one or both of these coefficients results in some measure of control of the tube wall temperature. This control can be employed to either increase or decrease the temperature of one of the process streams, i.e. either internal flow through the tubes or external flow over the outer surfaces of the tubes, for a given tube wall temperature, or to reduce the tube wall temperature for a particular process stream temperatures.
Heat exchangers frequently involve change of phase, e.g., water is sufficiently heated so as to be transformed to steam and steam is sufficiently cooled to become water. Augmented heat transfer is frequently desired in these applications; e.g., in steam condensers the internal thermal resistance of the single phase coolant can be three times as high as the external resistance. A similar need for augmented heat transfer arises in the boilers of steam bottoming cycles; in these units heat is supplied from the exhaust gases of a diesel engine or gas turbine, involves a low heating rate and thus requires a large heat transfer area unless the heat transfer can be augmented. In both boiling and condensing applications heat transfer is generally limited by the transfer characteristics of the single phase fluid. If this limitation is removed by suitable augmentation, the performance of a heat exchanger or condenser is then determined by two phase heat transfer characteristics.
The use of swirl to augment heat transfer is well known and may be established in a variety of ways. For example, twisted-tape inserts have been employed which provide means for increasing the heat transfer within the interior of tubing. Tangential injection of the fluid at the entrance to a tube has also been employed to provide an initial rotation which decays in the downstream direction but provides augmented heat transfer while it prevails.
The general objective of improvement to heat exchange tubing is the increase of the heat transfer relative to the frictional flow loss. For single phase flow on either side of a tube this is expressed by the Colburn factor. EQU 2.sub.j /f=2 N.sub.s P.sub.r.sup.2/3 /f
Where:
N.sub.s =Stanton Number PA1 P.sub.r =Prandtl Number PA1 f=Fanning friction factor PA1 .epsilon..sub.h =turbulent exchange coefficient for heat PA1 .epsilon..sub.m =Turbulent exchange coefficient for momemtum PA1 .tau..sub.t =.epsilon..sub.m /.epsilon..sub.h PA1 P is the perimeter of the enhanced and extended tube PA1 N.sub.s is the Stanton Number h/C.sub.p .rho.u PA1 W is the pumping power PA1 .lambda. is the friction coefficient PA1 C.sub.p is the specific heat at constant pressure PA1 u is the mean velocity PA1 h is the surface conductance coefficient PA1 .rho. is the density of the fluid
The Colburn factor is numerically equal to 1 for a smooth tube. Therefore, a tube performance factor can be defined as the ratio of the Colburn factor of an enhanced tube relative to a smooth tube. ##EQU1##
This performance factor can be related to the ratio of the turbulent exchange coefficients of heat relative to momentum, (the reciprocal of the turbulent Prandtl Number). EQU .zeta.=.epsilon..sub.h /.epsilon..sub.m =1/.tau..sub.t
Where:
The present state of the art of enhanced tubing for heat exchangers has an upper bound of 1 for the tube performance factor (or ratio of turbulent diffusivity of heat to that of momentum) which is the value for a smooth tube.
One attempt to provide improved heat-transfer coefficient is disclosed in U.S. Pat. No. 3,612,175 which shows an improvement in overall heat transfer coefficient by a factor of approximately 1.6 at a cost of increased pressure drop by a factor of 3.5 as compared to the heat transfer and pressure drop of a smooth tube. The ratio of increase in heat transfer is less than the increase in pressure drop relative to a smooth tube. Pat. No. 3,612,175 recognizes that it is highly desirable to provide for improved condenser tubing in which the heat transfer is maximized but the increase in the pressure drop kept as low as possible.
It can be established by mathematical analysis that the index for heat transfer per unit pumping power for a tube having a spirally fluted wall, which tube may thereby be defined as being enhanced and extended, relative to a smooth round tube is:
For fixed heat transfer; ##EQU2## Where: Q is the rate of heat transfer
For fixed coolant flow rate; ##EQU3##
It can also be established that the ratio of Stanton Number and friction factor or coefficient relates to the ratio of the turbulent exchange coefficients of heat and momentum as E.sub.h /E.sub.m =N.sub.s /.lambda.. From this it follows that an increase in the ratio of Stanton Number to friction coefficient, or alternatively, the ratio of turbulent exchange coefficient for heat to that of momentum, greater than that of a round smooth tube (that has a value of one) is highly desirable, particularly if the heat transfer area is increased as well. However, there can be an advantage when the frictional increase is greater than the Stanton Number increase if the frictional increase is less than the product of the cube of the Stanton Number increase and the heat transfer area increase for the case of a given rate of heat transfer.
It is generally recognized that in heat transfer tubes most of the resistance to heat transfer and most of the skin friction is associated with the fluid adjacent the wall of the tube, the so-called laminar sublayer where the transport of heat and momentum are dependent on the molecular transport; the thermal conductivity and the viscosity. Increasing the transport of heat can only be achieved in a straight round tube by increasing the shear through an increase of fluid velocity in the tube or increasing the level of turbulence by roughening the surface of the round tube. Either of these methods are bounded in their performance by the value of E.sub.h /E.sub.m =1. However, the creation of an instability in the vicinity of the laminar boundary sublayer can result in a greater increase in the turbulent exchange coefficient of heat relative to the turbulent exchange coefficient of momentum.